How rare is this then?

Forums Computing How rare is this then?

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    Posted by Graham Relf at 20:44 on 2011 Mar 09

    At the end of May all the major planets (and Pluto) except Saturn will be strung out before dawn in order of distance from the Sun: (image from our applet at anyone know how rare an event this is?Unfortunately it is not favourably positioned for UK observers.


    Posted by Sheridan Williams at 09:00 on 2011 Mar 10

    We need to see if we can persuade Jean Meeus to work on this.


    Posted by Steve Holmes2 at 17:15 on 2011 Mar 13

    I suspect alignments of this sort will be more common than one might think, but will definitely come in "seasons".Given the slow motion across the sky of the gas giant planets, it is clear that once the J-S-U-N-(P) order has been established it will persist for many years. Conversely, as Mercury and Venus move very quickly (one circuit of the sky per year, approximately) in this time there will be many occasions for the order Me-V to happen while they are "to the right of" the sun but "to the left of" Jupiter. The only problem child is thus Mars, as its motion is quite fast and so its oppositions, for example, shift by over 45deg per occasion.The problem might thus reduce to what is the maximum angle allowed between Mercury and Neptune/Pluto? More than 180deg and all planets will not be simultaneously visible, but they will still be in order, nonetheless.For example, on page 348 of "More Mathematical Astronomy Morsels" (aka Morsels II), Jean Meeus tabulates the occasions from 1979 to 2020 when all five naked-eye planets are simultaneously visible in the night sky. This shows that in December 2004 and January 2005 they are arranged in order of distance. Further checks with my astronomy programme shows that Uranus, Neptune and Pluto are also in order, and to the west of Saturn. All planets are thus in the correct order. However! There is a very large gap between Saturn and Uranus and so the outer three are not visible at the same time as the inner five, and even in the best case (11th December) by the time you get to Pluto the arc is almost 360deg. Does this count, therefore?[Amazingly, for a couple of hours before midnight on 11th Dec, the moon is between the Sun and Mercury and so every one of the "heavenly bodies" is then in the correct order! This will of course not be visible at all in the UK, however.]While J-S-U-N-P will persist for many years, Jupiter will get more than 180deg in front of Saturn about 10yrs after being close to it. It will then be to the east again after about another 10yrs, but the pair will now both be to the west of the U-N-P grouping. It will be another 20yrs (the Jupiter/Saturn conjunction period) until they both emerge to the east of the U-N-P grouping again (but of course much further east). I would thus expect that there would have been "correct order" groupings 20 or 40yrs before the 2004/5 set – before, because Saturn was already well to the east of Uranus in 2004/5. Anyone care to check?


    Posted by Graham Relf at 15:07 on 2011 Mar 14

    Thanks for your comments Steve. I think they are all quite valid. I have done some analysis myself and written up the result as the start of a new "Morsels" page on the Computing Section site: will see that it does not quite answer my original question but a more restricted one: all major planets in the right order.Would you, or anyone, like to contribute further morsels, or ideas for subjects?


    Posted by Steve Holmes2 at 16:04 on 2011 Mar 14

    Nice work Graham. Calculation trumps logic every time, I fear! I had also done a bit more work on this (manually, not using detailed calculation) and had already found the Nov 2002 and Apr 2041 events. I was only really looking for alignments in the evening sky so I would not have found some of the cases you did anyway.This work showed that the 780day synodic period of Mars was as important as the almost 20yr conjunction period of Jupiter/Saturn. This can be seen in your events in 811, 813 and 815 and other 2yr-apart pairings. I also found I had underestimated the role of Uranus: in a 40yr period it moves quite a lot! I think this is probably what accounts for the large gap between 2041 and 2154: the outer giants are simply not close enough together then to allow the others to fit into the bit of the sky that’s left. The pairs of events a couple of months apart seem to be due to the rapid motion of Mercury, re-appearing to the appropriate side of the sun before Venus has had time to move out of alignment.Your work does show though that my hunch that such alignments are not all that rare seems to be true, particularly if one further restricts oneself to the five major planets. Pity the next one isn’t until 2041 though!As to "morsels" more generally, you might have noticed that I posed an almost exactly similar question myself on the forum some time ago (with no replies at all!!). As I said at the time, I have set up a section of my personal website as a "Theory" section, in which I have placed a number of articles in the style of Jean Meeus’ books. It can be found at Some of the articles are very (very!) long but if you think they might survive the journey to the BAA Computing site then I would be honoured to port them across.


    Posted by Graham Relf at 14:01 on 2011 Mar 30

    Callum raised a further question in his Sky Notes in the latest Journal. So I have added another page about that:

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